Recent Results

In recent years, considerable concern has been raised about ordering and disordering of charge, spin, and orbital in 3d-electron system, since it has been recognized that they play important roles in various interesting phenomena such as metal-insulator transition, high-T_c superconductivity, and colossal magnetoresistance. In particular, a large number of studies have been performed on the charge-orbital ordering of e_g electrons in mixed-valent manganites. We have successfully observed the transverse and sinusoidal structural modulations in charge-orbital ordered manganites, Nd_1-xCa_1+xMnO₄(0.55≦x≦0.75), by low-temperature HREM. Single-layered manganites Nd_1-xCa_1+xMnO₄have distorted K₂NiF₄ type fundamental structures based on alternate stacking of MnO₂ sheet and rock-salt type (Nd,Ca)₂O₂layer. In this system, the concentration of e_g electrons on Mn site (n_e) can be controlled by the atomic ratio of divalent Ca to trivalent Nd and be described as 1-x.

The polycrystalline samples were synthesized by conventional solid-state reaction in air. Thin specimens for HREM investigation were prepared by crushing the samples. The HREM observation was conducted with a Hitachi HF-3000 field-emission transmission electron microscope, operated at 300 kV, and equipped with a low-temperature sample holder.

The system exhibits the formation of superstructure related to the ordering of charge and orbital of e_g electrons at low temperatures, as well as other many manganites. We display in Fig.1 the ED patterns for the x=0.69 sample [Fig.1(a)] at 340K along [001], [Fig.1(b)] at 80K along [001], and [Fig.1(c)] at 80K along [010]. The pattern at 80K along [001] clearly shows a series of sharp statellite spots around the fundamental Bragg ones. The superlattice reflections appear for all doping level of 0.55≦x≦0.75, or commensurate and incommensurate e_g electrons concentration of 0.25≦n_e≦0.45. The wave vector of the structural modulation can be described as k_s=(1-x)a* =(1-x)k₁₁₀^t/2, which is shown in Fig.1(d). Figure 1(e) shows the temperature dependence of the superlattice reflection intensity for the x=2/3 sample. Superlattice spots are clearly visible even at room temperature for the composition around x=2/3. Weak satellite spots appearing below ~330K indicate the onset of the charge-orbital ordering (T_CO). The suppresssion of magnetization toward lower temperatures has been also observed at T_CO.

In order to reveal the structural modulation, we observed the low-temperature high-resolution images. Figure 2(a) shows the HREM image projected along [001] at 80K (<T_CO) for the sample with commensurate doping level of x=2/3 (n_e=1/3). The image shows superlattice fringes and nearly sinusoidal transverse modulation of the crystal structure along the a axis ([110]^t) with the same commensurate period of 3a (6d₁₁₀^t). If we select a position of Mn atom for the origin of atomic position parameter along [110]^t (x) and give a sinusoidal atomic displacement described asΔy=b_maxsin(2πx/6d₁₁₀^t), we can acquire the superstructure model nearly consistent with “Wigner-crystal” model as shown in Fig.2(b). We show in Fig.3(a) the HREM image at 80K (<T_CO) for x=0.7. The image exhibits superlattice fringes and nearly sinusoidal transverse modulation along the a axis with the same incommensurate period of ~3.3a (~6.7d₁₁₀^t). The amplitude of MnO₆distortion is modulated along [110]^t, but the shapes of the octahedra can not be classified because of the incommensurate periodicity, as shown in Fig.3(b).

Based on the observed transverse and sinusoidal structural distortion in both the commensurate and incommensurate carrier concentration, let us discuss the modulation of charge and orbital state in the present system. A possible “charge-density wave” in over-doped single-layered manganites has been proposed, where the successive change in the amplitude of the Jahn-Teller distortion in MnO₆ octahedra with the position has been interpreted as the modulation of the manganese valence, that is, the density of e_g electron. We illustrate in Fig. 4 such a CDW state. Figure 4(a) shows the description of the orbital state by the pseudo-spin space. A motion of the pseudo-spin is assumed to be confined in the xz plane, and θ_i describes the orbital state at the i site as follows

|θ_i>=cos(θ_i/2)|x²-y²>+sin(θ_i/2)|3z²-r²> .

If we consider the pure CDW state, the orbital state toward the direction perpendicular to the stripe varies as indicated alternately by the two straight arrows (1) in Fig.4(a). The variations of both Mn valence and θ are plotted as a function of position in the left panels of Fig. 4(b). Although the Mn valence (or density of e_g electron) successively varies with the position, the change in θ is “discrete” between ±π/3. Here, let us propose the possibility of “orbital density wave” state, which is recently discussed by Koizumi et al. We can also interpret the observed modulated structure as the “ODW” state. In pure ODW state, the density of e_g electron is constant. However, the orbital state varies on the circular arrow (2) in Fig.4(a), that is, oscillates successively between θ=±π/3, as shown in the right panels of Fig.4(b). It is possible that the real charge-orbital state in the single-layered manganites takes a mean position between the above two extreme situations.